Análisis de Datos 1
Curso: Métodos Avanzados en Minería de Datos
Métodos Exploratorios desde la consola de R (Clustering, Aprendizaje no Supervisado)
Análisis en Componentes Principales
# Valores de los gráficos por defecto
mi.tema <- theme_grey() + theme(panel.border = element_rect(fill = NA,color = "white"), plot.title = element_text(hjust = 0.5))Biplots
Ejemplo Estudiantes
setwd("~/Google Drive/MDCurso/Datos")
Datos <- read.table('EjemploEstudiantes.csv', header=TRUE, sep=';',dec=',',row.names=1)
modelo <- prcomp(Datos,scale. = TRUE,center = TRUE)
modelo## Standard deviations (1, .., p=5):
## [1] 1.70095552 1.27618589 0.58872409 0.35016062 0.09429419
##
## Rotation (n x k) = (5 x 5):
## PC1 PC2 PC3 PC4 PC5
## Matematicas -0.5266440 -0.27049630 0.43820071 -0.26121779 -0.6238776
## Ciencias -0.4249362 -0.50807221 0.04049491 0.67362724 0.3253895
## Espanol -0.3591470 0.56208159 0.56227583 -0.07008647 0.4837473
## Historia -0.3526975 0.58648985 -0.39418032 0.44664495 -0.4204335
## EdFisica 0.5373018 0.09374599 0.57862603 0.52305619 -0.3067941Tipos de Gráficos
Tipos de Gráficos
ACP Usando FactoMineR
Tipos de Gráficos
Por defecto (FactoMineR)
Usando factoextra
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 10 individuals, described by 5 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. for the variables"
## 4 "$var$cor" "correlations variables - dimensions"
## 5 "$var$cos2" "cos2 for the variables"
## 6 "$var$contrib" "contributions of the variables"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "summary statistics"
## 12 "$call$centre" "mean of the variables"
## 13 "$call$ecart.type" "standard error of the variables"
## 14 "$call$row.w" "weights for the individuals"
## 15 "$call$col.w" "weights for the variables"## eigenvalue percentage of variance
## comp 1 2.893249673 57.8649935
## comp 2 1.628650425 32.5730085
## comp 3 0.346596049 6.9319210
## comp 4 0.122612460 2.4522492
## comp 5 0.008891393 0.1778279
## cumulative percentage of variance
## comp 1 57.86499
## comp 2 90.43800
## comp 3 97.36992
## comp 4 99.82217
## comp 5 100.00000## $coord
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Matematicas 0.8957980 -0.3452036 0.25797931 -0.09146818 0.05882803
## Ciencias 0.7227976 -0.6483946 0.02384033 0.23587773 -0.03068234
## Espanol 0.6108931 0.7173206 0.33102532 -0.02454152 -0.04561456
## Historia 0.5999227 0.7484701 -0.23206345 0.15639747 0.03964443
## EdFisica -0.9139265 0.1196373 0.34065108 0.18315368 0.02892890
##
## $cor
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Matematicas 0.8957980 -0.3452036 0.25797931 -0.09146818 0.05882803
## Ciencias 0.7227976 -0.6483946 0.02384033 0.23587773 -0.03068234
## Espanol 0.6108931 0.7173206 0.33102532 -0.02454152 -0.04561456
## Historia 0.5999227 0.7484701 -0.23206345 0.15639747 0.03964443
## EdFisica -0.9139265 0.1196373 0.34065108 0.18315368 0.02892890
##
## $cos2
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Matematicas 0.8024540 0.11916550 0.0665533242 0.0083664287 0.0034607374
## Ciencias 0.5224364 0.42041555 0.0005683612 0.0556383052 0.0009414059
## Espanol 0.3731904 0.51454884 0.1095777630 0.0006022863 0.0020806881
## Historia 0.3599073 0.56020745 0.0538534429 0.0244601695 0.0015716811
## EdFisica 0.8352616 0.01431309 0.1160431572 0.0335452699 0.0008368811
##
## $contrib
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Matematicas 27.73539 7.3168250 19.2019858 6.8234735 38.92233
## Ciencias 18.05708 25.8137375 0.1639838 45.3773665 10.58783
## Espanol 12.89866 31.5935718 31.6154103 0.4912113 23.40115
## Historia 12.43955 34.3970346 15.5378121 19.9491712 17.67643
## EdFisica 28.86932 0.8788311 33.4808079 27.3587774 9.41226## $coord
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Lucia 0.32306263 1.7725245 1.19880074 -0.05501532 0.003633384
## Pedro 0.66544057 -1.6387021 0.14547628 -0.02306468 -0.123377296
## Ines 1.00254705 -0.5156925 0.62888764 0.51644351 0.142875824
## Luis -3.17209481 -0.2627820 -0.38196027 0.67777691 -0.062503554
## Andres -0.48886797 1.3654021 -0.83523570 -0.15579197 0.123367255
## Ana 1.70863322 -1.0217004 -0.12707707 0.06683295 0.025291503
## Carlos 0.06758577 1.4623364 -0.50624044 -0.11792847 0.013123980
## Jose 2.01185516 -1.2758646 -0.54215002 -0.19778670 0.017434170
## Sonia -3.04203029 -1.2548807 0.44882861 -0.63999876 0.037884840
## Maria 0.92386867 1.3693593 -0.02932977 -0.07146746 -0.177730107
##
## $cos2
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Lucia 0.022270827 0.670420670 0.306659839 0.0006458478 2.816992e-06
## Pedro 0.139905502 0.848430539 0.006686527 0.0001680781 4.809354e-03
## Ines 0.514468899 0.136122895 0.202439714 0.1365196756 1.044882e-02
## Luis 0.936851990 0.006429392 0.013583605 0.0427712757 3.637375e-04
## Andres 0.084139511 0.656353715 0.245603703 0.0085448999 5.358172e-03
## Ana 0.732686110 0.261979570 0.004052795 0.0011209894 1.605349e-04
## Carlos 0.001892733 0.886081139 0.106192189 0.0057625700 7.136907e-05
## Jose 0.673612108 0.270910359 0.048916504 0.0065104446 5.058468e-05
## Sonia 0.808829929 0.137636943 0.017607237 0.0358004434 1.254472e-04
## Maria 0.308554271 0.677869212 0.000310977 0.0018464085 1.141913e-02
##
## $contrib
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Lucia 0.36073437 19.2910834 41.46392357 0.24684974 0.01484748
## Pedro 1.53049754 16.4881591 0.61060555 0.04338706 17.11987788
## Ines 3.47395038 1.6328779 11.41096846 21.75259335 22.95871968
## Luis 34.77814436 0.4239976 4.20932799 37.46613853 4.39379307
## Andres 0.82603273 11.4470414 20.12771563 1.97950024 17.11709152
## Ana 10.09047896 6.4094282 0.46591936 0.36428947 0.71941493
## Carlos 0.01578791 13.1300601 7.39418080 1.13423412 0.19371414
## Jose 13.98967133 9.9949649 8.48038057 3.19050613 0.34184774
## Sonia 31.98461714 9.6688984 5.81215853 33.40593699 1.61421395
## Maria 2.95008527 11.5134890 0.02481953 0.41656436 35.52647960
##
## $dist
## Lucia Pedro Ines Luis Andres Ana Carlos Jose
## 2.164804 1.779065 1.397736 3.277258 1.685356 1.996135 1.553497 2.451273
## Sonia Maria
## 3.382478 1.663200Individuos y variables mal representados
setwd("~/Google Drive/MDCurso/Datos")
# Ejemplo de las importaciones de México
Datos <- read.table('ImportacionesMexico.csv', header=TRUE, sep=';',dec=',',row.names=1)
res<-PCA(Datos, scale.unit=TRUE, ncp=5, graph = FALSE)
cos2.ind<-(res$ind$cos2[,1]+res$ind$cos2[,2])*100
cos2.ind## 1979 1980 1981 1982 1983 1984
## 96.1000354 86.9743777 80.6523653 70.7456314 65.6042706 85.9034700
## 1985 1986 1987 1988
## 75.1710823 81.9688762 4.9898384 0.8100985Tipos de Gráficos
Por defecto (FactoMineR)
# Grafica los individuos que tengan cos2 >= 0.1 (10%)
plot(res, axes=c(1, 2), choix="ind",col.ind="red",new.plot=TRUE,select="cos2 0.1")
Usando factoextra
# Grafica los individuos que tengan cos2 >= 0.1 (10%)
fviz_pca_ind(res, pointsize = 5, pointshape = 21, fill = "#E7B800", repel = TRUE, select.ind = list(cos2 = 0.1),ggtheme = mi.tema)
## Costa.Rica El.Salvador Guatemala Honduras Nicaragua Panama
## 73.87060 89.22701 71.89417 67.23724 77.57747 90.95865Tipos de Gráficos
Interpretando los individuos mal representados
Plano y círculo 1-3
Por defecto (FactoMineR)
# Grafica los individuos que tengan cos2 >= 0.1 (10%)
plot(res, axes=c(1, 3), choix="ind",col.ind="red",new.plot=TRUE,select="cos2 0.1")
Por defecto (FactoMineR)
# Grafica las variables que tengan cos2 >= 0.1 (10%)
plot(res, axes=c(1, 3), choix="var",col.var="blue",new.plot=TRUE,select="cos2 0.1")
Se observa que en los años 1987 y 1988 las importaciones de Mérxico fueron fuertes en Costa Rica y Honduras.
Análisis en Componentes Principales (ACP) con Variables Categóricas y Numéricas mezcladas
Es completamente incorrecto hacer un ACP, una CJ o un k-medias con variables cualitativas simplemente convirtiendo las categorías a códigos, por ejemplo, cambiando Femenino por un 1 y Masculino por un 2 porque no tiene ningún el álgebra ni las fórmulas de distancia. Las opciones son:
ACP Usando variables “Dummy” (Códigos disyuntivos completos)
Usando el paquete dummies
dummies-1.5.6 provided by Decision Patternssetwd("~/Google Drive/MDCurso/Datos")
Datos <- read.csv("EjemploEstudiantesAmpliado.csv",header=TRUE, row.names=1, sep=";", dec=",")
Datos Matematicas Ciencias Espanol Historia EdFisica Sexo Provincia
Lucia 7.0 6.5 9.2 8.6 8.0 F Puntarenas
Pedro 7.5 9.4 7.3 7.0 7.0 M Puntarenas
Ines 7.6 9.2 8.0 8.0 7.5 F Puntarenas
Luis 5.0 6.5 6.5 7.0 9.0 M Puntarenas
Andres 6.0 6.0 7.8 8.9 7.3 M Puntarenas
Ana 7.8 9.6 7.7 8.0 6.5 F Puntarenas
Carlos 6.3 6.4 8.2 9.0 7.2 M Puntarenas
Jose 7.9 9.7 7.5 8.0 6.0 M Puntarenas
Sonia 6.0 6.0 6.5 5.5 8.7 F Puntarenas
Maria 6.8 7.2 8.7 9.0 7.0 F Puntarenas
Conducta
Lucia 3
Pedro 2
Ines 2
Luis 1
Andres 2
Ana 3
Carlos 1
Jose 1
Sonia 2
Maria 3'data.frame': 10 obs. of 8 variables:
$ Matematicas: num 7 7.5 7.6 5 6 7.8 6.3 7.9 6 6.8
$ Ciencias : num 6.5 9.4 9.2 6.5 6 9.6 6.4 9.7 6 7.2
$ Espanol : num 9.2 7.3 8 6.5 7.8 7.7 8.2 7.5 6.5 8.7
$ Historia : num 8.6 7 8 7 8.9 8 9 8 5.5 9
$ EdFisica : num 8 7 7.5 9 7.3 6.5 7.2 6 8.7 7
$ Sexo : Factor w/ 2 levels "F","M": 1 2 1 2 2 1 2 2 1 1
$ Provincia : Factor w/ 1 level "Puntarenas": 1 1 1 1 1 1 1 1 1 1
$ Conducta : int 3 2 2 1 2 3 1 1 2 3[1] 10 8Warning in model.matrix.default(~x - 1, model.frame(~x - 1), contrasts =
FALSE): non-list contrasts argument ignored'data.frame': 10 obs. of 8 variables:
$ Matematicas: num 7 7.5 7.6 5 6 7.8 6.3 7.9 6 6.8
$ Ciencias : num 6.5 9.4 9.2 6.5 6 9.6 6.4 9.7 6 7.2
$ Espanol : num 9.2 7.3 8 6.5 7.8 7.7 8.2 7.5 6.5 8.7
$ Historia : num 8.6 7 8 7 8.9 8 9 8 5.5 9
$ EdFisica : num 8 7 7.5 9 7.3 6.5 7.2 6 8.7 7
$ Sexo.F : int 1 0 1 0 0 1 0 0 1 1
$ Sexo.M : int 0 1 0 1 1 0 1 1 0 0
$ Conducta : int 3 2 2 1 2 3 1 1 2 3
- attr(*, "dummies")=List of 1
..$ Sexo: int 6 7[1] 10 8 Matematicas Ciencias Espanol Historia EdFisica Sexo.F Sexo.M
Lucia 7.0 6.5 9.2 8.6 8.0 1 0
Pedro 7.5 9.4 7.3 7.0 7.0 0 1
Ines 7.6 9.2 8.0 8.0 7.5 1 0
Luis 5.0 6.5 6.5 7.0 9.0 0 1
Andres 6.0 6.0 7.8 8.9 7.3 0 1
Ana 7.8 9.6 7.7 8.0 6.5 1 0
Conducta
Lucia 3
Pedro 2
Ines 2
Luis 1
Andres 2
Ana 3
